Question

if (5/8)power 4n-4 =(25/64)power 3n+4 ,find the value of n.​

Answer 1

Given:-

${( \frac{5}{8} )}^{4n - 4} = {( \frac{25}{64}) }^{3n + 4}$

To find:-

• The value of n.

Solution:-

${( \frac{5}{8}) }^{4n - 4} = {( \frac{25}{64}) }^{3n + 4}$

$\implies ( \frac{5}{8})^{4n - 4} = (\frac{5}{8})^{2 \times (3n + 4)}$

$\implies {( \frac{5}{8} )}^{4n - 4} = {( \frac{5}{8} )}^{6n + 8}$

Comparing base, we get,

$4n - 4 = 6n + 8$

$\implies 6n - 4n = - 8 - 4$

$\implies 2n = - 12$

$\implies n = - \frac{12}{2}$

$\implies n = - 6$

Answer:-

The value of n is 6.

$n = 6$